Tolerated Error in Plaxis 2D

Hi,

1)
PLAXIS doesn't determine the exact solution, because if it would be able to determine the exact solution then we wouldn't need a tolerated error.
PLAXIS tries to reach equilibrium between the sum of the external forces applied to the model (loads, weight) and the integral of the internal stresses in the soil and structural elements. The error calculated is the difference between internal stresses and the external loads as percentage of the external loads.

2)
Real equiibrium means that the integrated internal stresses are equal to the sum of the external load, hence the error is zero.  In principle if the error is not equal to zero there is no real equlibrium, but if the error is like 0.01 then of course there is almost equilibrium. But an error of for instance 01. hence 10%, means that in principal the internal stresses can be 10% too small compared to the applied load and the calculation would consider that fine. But of course if the stresses are really 10% to small then we may underestimated the safety factor with 10%.
So in principle if a tolerated error of 0.01 is a problem and 0.03 one should investigate why. If indeed there is true geotechnical failiure for an error of 0.01 one should not use 0.03 because then the soil doesn't fail for numerical reasons. And even if it seems to be just a numerical problem that makes the calculation have a problem with an error of 0.01 there are better ways to solve it depending on the exact cause of the problem. For instance if there's a problem with one element in the mesh slightly refining the mesh there may help, or switching of arc-length control. So whenever this problem occurs one should look for the cause and not just surpass it by increasing the tolerated error a bit.

Best regards,

Dennis Waterman

Thanks, dear Dennis for your answer. This helps me too much. 

But I have a question regarding soils failure. Is there any output stating about this situation or implying it? Or it is a judgment based on the global presentation of the outputs regarding the displacements field?

Dear Idrassa,

Failure in PLAXIS is determined based on the fact that increasing the external load does not lead to increased stresses anymore. Hence, the difference between the externally applied load and the internal stresses does not reduce to zero. When the calculation stops one can usually see from the numerical parameters that SMstage < 1  (hence not all load was applied) while  CSP is almost zero (hence any change of strains is almost completely plastic and not elastic).

Practically speaking failure can be seen through the incremental displacements, incremental shear strains and/or plastic points plots. 

With kind regards,

Dennis Waterman

Hi Dear Dennis,

I still have confusion about incremental displacement and phase displacement. According to my understanding of the instructions in the manuals, the incremental disp is about a particular Step, and the phase disp on the other hand consists of the displacements occurring during the whole phase. But how can I be sure to be analyzing the right step given there are many steps in a given phase? Even if the stored step is the more efficient one (according to the PLAXIS Manual), I still don't understand the difference observed between this incremental disp and the phase displacement.

Then, isn't it more relevant to evaluate failure on the basis of phase displacements instead of incremental ones? 

Lastly, I have to make a simulation using pseudo-static analysis, so I have chosen to use a consolidation calculation type. Is this choice right and do you have any pseudo-static analysis tutorial for me?

Thanks in advance. 

Dear Idrissa,

By default when showing incremental displacements those are from the last step of the phase. Which makes sense, because if PLAXIS detects failure then it stops calculating and the last step of the phase is the one that occured the failure in.  However, if you want to you can see results from intermediate steps by changing the phase list at the toolbar in PLAXIS Output to a step list by clicking on the button just left of the phase list:





Phase displacements are not suitable for detecting failure, because in a calculation phase there can be large displacement not  related to failure. For instance when constructing an embankment on soft soil, there will be large settlements so large phase displacement. But somewhere during the construction process the embankment may fail, which means that in that step the incremental displacement will be large only in the failure zone while the phase displacements will be large everywhere due to the settlements prior to failure.
Let's say you do a project with 4 phases and each phase takes 10 steps to solve. So Phase 1 is step 1-10, Phase 2 is step 11-20 etc.  When looking at Phase 3,
 - the default incremental displacement is the change of displacement that occured in step 30.
 - the phase displacement is the change of displacement in Phase 3, which is the sum of the incremental displcements of steps 21-30.
 - the total displacement is the sum of all displacements, hence the sum of the phase displacements of Phase 1, 2 and 3, which is equal to the sum of the incremental displacements of steps 1 - 30.

I'm wondering why you would choose a consolidation phase for a pseud-static analysis? Consolidation is used in case excess pressure have to be dissipated or when loading takes place that is not so fast that it can be considered perfectly undrained and not so slow that it can be considered perfectly drained. It's unrelated to pseudo-static analysis.

For a pseudo-static phase just use a Plastic phase and then in the Model Explorer under Model Conditions activate the option "PseudoStatic" and specify the horizontal and vertical acceleration.

With kind regards,

Dennis Waterman

Dear Idrissa,

By default when showing incremental displacements those are from the last step of the phase. Which makes sense, because if PLAXIS detects failure then it stops calculating and the last step of the phase is the one that occured the failure in.  However, if you want to you can see results from intermediate steps by changing the phase list at the toolbar in PLAXIS Output to a step list by clicking on the button just left of the phase list:





Phase displacements are not suitable for detecting failure, because in a calculation phase there can be large displacement not  related to failure. For instance when constructing an embankment on soft soil, there will be large settlements so large phase displacement. But somewhere during the construction process the embankment may fail, which means that in that step the incremental displacement will be large only in the failure zone while the phase displacements will be large everywhere due to the settlements prior to failure.
Let's say you do a project with 4 phases and each phase takes 10 steps to solve. So Phase 1 is step 1-10, Phase 2 is step 11-20 etc.  When looking at Phase 3,
 - the default incremental displacement is the change of displacement that occured in step 30.
 - the phase displacement is the change of displacement in Phase 3, which is the sum of the incremental displcements of steps 21-30.
 - the total displacement is the sum of all displacements, hence the sum of the phase displacements of Phase 1, 2 and 3, which is equal to the sum of the incremental displacements of steps 1 - 30.

I'm wondering why you would choose a consolidation phase for a pseud-static analysis? Consolidation is used in case excess pressure have to be dissipated or when loading takes place that is not so fast that it can be considered perfectly undrained and not so slow that it can be considered perfectly drained. It's unrelated to pseudo-static analysis.

For a pseudo-static phase just use a Plastic phase and then in the Model Explorer under Model Conditions activate the option "PseudoStatic" and specify the horizontal and vertical acceleration.

With kind regards,

Dennis Waterman

Okey I see. Thanks.

My choice to use consolidation was in order to take time into account, so for pore pressure analysis, I decided to use pressure from previous phase. In fact, I'm trying to analyze the stabilité of a Dam under the full reservoir and pseudo-static acceleration. 

Dear Idrissa,

I see what you would like to do, but the problem is that the applied accelerations influence the consolidation process. So the stability in time you would calculate may be based on a pore pressure distribution that in reality will not occur because in reality there is no constant acceleration for the whole duration of the consolidation time.
If you're interested in the stability in time, it would probably be better to cut the consolidation period in a couple of consecutive consolidation phases (let's say of a week each) and do a pseudo-static analysis (plastic, undrained) after each week of consolidation. Then you know the stability is determined from the correct pore pressure distribution.

With kind regards,

Dennis Waterman

Dear Dennis,

I understand what you explain. But what I did is not applying the acceleration during the whole consolidation time. It's another calculation phase especially for the pseudo-static analysis of a given situation. Then I entered a very short time interval (10e-3 day). Here's a screenshot of the passage.  

 This way, the calculations do converge while they do not in plastic calculation. 

Nevertheless, I have done the simulation accordingly to your advice. But when I inspect the outputs, I'm a little skeptical. There is no really relevant plot and values implying a failure for me.

When I analyze the plots of displacement, I wonder if there are not some nodes that are not correctly computed, because of the irregularity of the displacements field (see the second screenshot). Note that in this screenshot showing the displacements plot the calculation type was plastic and didn't converge.  

Dear Idrissa,

Just 2 short remarks before the weekend

1) The pseudostatic phases should not be part of the calculation sequence, they should be like "side steps".  So after a pseudo-static analysis one should not continue with again consolidation with acceleration. I can't see from the screen shots if that is what you're doing because the pictures are too small.

2) Failure is not detected from displacement plaits, but from incremental displacement plots. If the plots don't show a clear failure then maybe there just isn't failure for that acceleration...

With kind regards,

Dennis Waterman

1- They are side-steps indeed, but with different acceleration magnitudes.

2-The fact is that for me the plot of incremental disp doesn't convince me about a failure. But I need the make a safety calculation for it. That's why It "should" converge...

Have a nice weekend and thank you very much.

Kindly, Idrissa